Pattern search algorithms, such as diamond search, hexagonal search and their variations, have been widely adopted by the block matching motion estimations in the modern video encoding systems. Recently we propose a weighting function (WF) to model the number of search points of a pattern search. Yet, WF fails to properly describe the behavior of the genetic pattern search algorithms due to some over-simplifications in their models. Therefore, we propose a refined weighting function (RWF) to more accurately describe both genetic and non-genetic pattern searches. In addition, we propose a new search algorithm, namely, the momentum directed genetic rhombus pattern search (MD-GRPS). It can accelerate the previous genetic rhombus pattern search by 8% on the average and this concept can be applied to the other genetic pattern searches.